Infinite Horizon Reflected Backward SDEs with Jumps and RCLL Obstacle

Abstract

In this article, we deal with the one-dimensional reflected backward stochastic differential equation with one or two barriers for infinite horizon when the noise is driven by a Brownian motion and an independent Poisson point process. The reflecting process is right continuous with left limits whose jumps are whatever. The authors prove existence and uniqueness of the solution by using a method based on a combination of penalization and the Snell envelope theory. Once more we use a contraction to show the result in the general framework.

Keywords:

• Infinite horizon
• Martingale representation theorem
• Penalization
• Poisson point process
• Reflected BSDEs

MS Classification (1991):

• 60H10
• 60H20
• 60H99